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Some of the iron pnictides show coexisting superconductivity andspin-density-wave order. We study the superconducting pairing instability inthe spin-density-wave phase. Assuming that the pairing interaction is due tospin fluctuations, we calculate the effective pairing interactions in thesinglet and triplet channels by summing the bubble and ladder diagrams takingthe reconstructed band structure into account. The leading pairinginstabilities and the corresponding superconducting gap structures are thenobtained from the superconducting gap equation. We illustrate this approach fora minimal two-band model of the pnictides. Analytical and numerical resultsshow that the existence of propagating magnons in the spin-density-wave phasestrongly enhances the pairing in both the singlet and the spin s_z=0 tripletchannel. Over a limited parameter range, a spin s_z=0 triplet p_x-wave state isthe dominant instability. It competes with various singlet states, which havemostly s^\pm-type structures. We analyze the effect of various symmetry-allowedinteractions on the pairing in some detail.

Superconducting pairing in the spin-density-wave phase of iron pnictides